## Inpainting using perfect patch graph

### Goal

• Validate our idea before trying to retrieve the graph

### Method

1. Create patch graph from the original image
3. Diffusion on patch graph (TV or Thikonov prior)

### Large surface inpainting

• Observed image error (L2-norm) : 6512
• Reconstruction error : TV 250, Thikonov 246

### Small surfaces inpainting

• Observed image error (L2-norm) : 9584
• Reconstruction error : TV 321, Thikonov 312

### Results

• TV and Thikonov priors work equally well for large or small holes
• Thikonov is however much faster (3s for 88 iterations vs 22s for 200 iterations for large hole)

## GSPbox for signal filtering on graph

Signal filtering on graph :

• Exact method using the Fourier basis (computationally intensive as it requires a full diagonalization of the Laplacian)
• Chebyshev approximation

Fourier basis :

• The eigenvectors form the basis, i.e. any signal (on this graph) can be represented as a linear combination of them
• The eigenvalues represent the squared frequency

## GSPbox

The Graph Signal Processing toolbox is a matlab toolbox that performs a wide variety of filtering on graphs. It can create all sorts of filterbanks including wavelets and Gabor. It is based on spectral graph theory and can scale to very large graphs thanks to the use of Chebysheff polynomial approximations. The toolbox is developed by LTS2 under the GPLv3.

I’ll use (and maybe even develop) this toolbox as part of my attempt to perform image inpainting using graphs (the GIIN semester project).

## PyUNLocBoX

PyUNLocBoX is a convex optimization toolbox using proximal splitting methods implemented in Python. It is a free software distributed under the BSD license and is a port of the Matlab UNLocBoX toolbox. I’ve started its development in spring 2014 while I was a Research Assistant at EPFL LTS2.

The code and documentation are accessible online. You can even download a ready-to-go package on PyPI. You may also check the continuous integration testing at Travis CI or the original UNLocBoX who inspired this software.